How to pass arbitrary floating-point data from Animation Nodes into a shader?
You can transfer any kind of data (float, integer, negative, greater than 1, etc.) from Animation Nodes to Shader (Material) with the help of UV Map Data Output node or Set Vertex Colors node but for this, you need Animation Nodes + Extra Nodes.



Method-1:
First, we have to find the total number of vertices for individual polygons using the Mesh Object Input node and Separate Polygons node. Then, Create Float List (the list you want to pass to the shader), and now we have to make its length equal to the total number of vertices of polygons which we can achieve with Fill List node (length = total number of vertices of polygons). Now, connect this final list to the UV Map Data Output node (Note: Create Float List's length &lt;= Total number of vertices),


We have stored the data in UV coordinates which we can access in the material (I have added the color ramp node to show the difference between the values of the passed list),
 

Blend File:





Method-2:
This is also doable with Set Vertex Colors node in Blender2.81x but node-tree is more complex and slower. Here is the example, in which first I have mapped the Float List to 0-1 range then passes it as vertex colors.


Then, in the material, I have re-mapped them to back their original values with the Map Range node,


Blend File: